Results 11 to 20 of about 793 (178)
On the convergence of generalized polynomial chaos expansions [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2011 A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures.
Oliver G. Ernst +3 more
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A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS [PDF]
International Journal for Uncertainty Quantification, 2019 Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion.
Yang, Xiu +3 more
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Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification
Journal of Computational Physics, 2023 We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the gradient (or sensitivity) of the Quantity of Interest with respect to the stochastic variables. This sensitivity is
Kyriakos Dimitrios Kantarakias +1 more
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Computation of higher‐order moments of generalized polynomial chaos expansions [PDF]
International Journal for Numerical Methods in Engineering, 2017 SummaryBecause of the complexity of fluid flow solvers, non‐intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for example. The objective function is commonly expressed in terms of moments of these quantities, such as the mean,
Savin, É., Faverjon, B.
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Performance Evaluation of Generalized Polynomial Chaos [PDF]
, 2003 In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the
Dongbin Xiu +3 more
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Applied Sciences, 2021 Stability is a well-known challenge for rotating systems supported by hydrodynamic bearings (HDBs), particularly for the condition where the misalignment effect and the parametric uncertainty are considered.
Xiaodong Sun +2 more
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Stochastic Optimal Trajectory Generation via Multivariate Polynomial Chaos [PDF]
2018 AIAA Guidance, Navigation, and Control Conference, 2018 This thesis presents a framework that has been developed in order to compute stochastic optimal trajectories.
Whittle L., Sagliano M.
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Pygpc: A sensitivity and uncertainty analysis toolbox for Python
SoftwareX, 2020 We present a novel Python package for the uncertainty and sensitivity analysis of computational models. The mathematical background is based on the non-intrusive generalized polynomial chaos method allowing one to treat the investigated models as black ...
Konstantin Weise +4 more
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Hyperchaotic Self-Oscillations of Two-Stage Class C Amplifier With Generalized Transistors
IEEE Access, 2021 This paper yields process of development, numerical analysis, lumped circuit modeling, and experimental verification of a new hyperchaotic oscillator based on the fundamental topology of two-stage amplifier.
Jiri Petrzela
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A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters
Complexity, 2018 The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications ...
Rugao Gao, Keping Zhou, Yun Lin
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